Extended Source Diffraction Effects Near Gravitational Lens Fold Caustics

Calculations are presented detailing the gravitational lens diffraction due to the steep brightness gradient of the limb of a stellar source. The lensing case studied is the fold caustic crossing. The limb diffraction signal greatly exceeds that due to the disk as a whole and should be detectable for white dwarf sources in our Galaxy and it's satellites with existing telescopes. Detection of this diffraction signal would provide an additional mathematical constraint, reducing the degeneracy among models of the lensing geometry. The diffraction pattern provides pico-arcsecond resolution of the limb profile.Comment: 19 pages including 17 figures, Accepted for publication in ApJ, Minor conceptual change from previous versio

Magnification relations in gravitational lensing via multidimensional residue integrals

We investigate the so-called magnification relations of gravitational lensing models. We show that multidimensional residue integrals provide a simple explanation for the existence of these relations, and an effective method of computation. We illustrate the method with several examples, thereby deriving new magnification relations for galaxy lens models and microlensing (point mass lensing).Comment: 16 pages, uses revtex4, submitted to Journal of Mathematical Physic

Fermions on Non-Trivial Topologies

An exact expression for the Green function of a purely fermionic system moving on the manifold $\Re \times \Sigma^{D-1}$, where $\Sigma^{D-1}$ is a $(D-1)$-torus, is found. This expression involves the bosonic analog of $\chi_n = e^{in\theta}$ corresponding to the irreducible representation for the n-th class of homotopy and in the fermionic case for D=2 and 3, $\chi_n$ is a measure of the statistics of the particles. For higher dimensions ($D \geq 4$), there is no analogue interpretation however this could, presumably, indicate a generation of mass as in quantum field theories at finite temperature.Comment: Some portions re-written, references added. To appear in PL

Near-infrared reddening of extra-galactic GMCs in a face-on geometry

[Abridged] We describe the near-infrared reddening signature of giant molecular clouds (GMCs) in external galaxies. In particular, we examine the E(J-H) and E(H-K) color-excesses, and the effective extinction law observed in discrete GMC regions. We also study the effect of the relative scale height of the GMC distribution to the color-excesses, and to the observed mass function of GMCs. We perform Monte Carlo radiative transfer simulations with 3D models of stellar radiation and clumpy dust distributions, resembling a face-on geometry. The scattered light is included in the models, and near-infrared color maps are calculated from the simulated data. The effective near-infrared reddening law, i.e. the ratio E(J-H)/E(H-K), has a value close to unity in GMC regions. The ratio depends on the relative scale height of GMCs, xi, and for xi values 0.1...0.75 we find the typical ratios of 0.6...1.1. The effective extinction law turns out to be very flat in GMC regions. We find the ratios of apparent extinctions of A(H)/A(K)=1.35...1.55 and A(J)/A(H)=1.15. The effect of the scattered flux on the effective reddening law, as well as on the effective extinction law, is significant. Regarding the GMC mass function, we find no correlation between the input and observed slopes of the mass functions. Rather, the observed slope reflects the parameter $\xi$ and the dynamical range of the mass function. We estimate that only a fraction of 10...20 % of the total mass of GMCs is recovered, if the observed color-excess values are transformed to masses using the Galactic reddening law. In the case of individual clouds the fraction can vary between ~0...50 %.Comment: 8 pages, 10 figures, accepted for publication in A&A. Added missing histograms in Fig.

The Transition from Welfare to Work

We consider the effects the child care market, child care vouchers, early childhood education programs, and welfare reforms have on welfare recipients in their transition from welfare to work. Specifically, we are interested in determining which factors encourage single mothers to move directly from welfare to work and which factors encourage the pursuit of additional schooling or job retraining before entering the labor market. Using Massachusetts data from July 1996 through August 1997, we find that the availability, quality, and cost of formal child care are all positively related to transiting directly from welfare to work. We also find that single mothers with older children are more likely to pursue a job and forego additional schooling, while single mothers with infants are more likely to advance their education before seeking employment.Welfare Reform, Child Care, Vouchers, Time Limits, Labor Supply

Segregation during directional melting and its implications on seeded crystal growth: A theoretical analysis

Directional melting of binary systems, as encountered during seeding in melt growth, is analyzed for concurrent compositional changes at the crystal-melt interface. It is shown that steady state conditions cannot normally be reached during seeding and that the growth interface temperature at the initial stages of seeded growth is a function of backmelt conditions. The theoretical treatment is numerically applied to Hg1-xCdXTe and Ga-doped Ge